If (a_1, b_1, c_1) and (a_2, b_2, c_2) are th | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The direction cosines of two lines are given as $(a_1, b_1, c_1)$ and $(a_2, b_2, c_2)$.Since these are direction cosines,we have the property $a_

Vedclass · Accepted Answer

$|a_1 a_2 + b_1 b_2 + c_1 c_2|$

Vedclass · Answer

(B) The direction cosines of two lines are given as $(a_1, b_1, c_1)$ and $(a_2, b_2, c_2)$.Since these are direction cosines,we have the property $a_1^2 + b_1^2 + c_1^2 = 1$ and $a_2^2 + b_2^2 + c_2^2 = 1$.The angle $	heta$ between two lines with direction cosines $(l_1, m_1, n_1)$ and $(l_2, m_2, n_2)$ is given by $\cos 	heta = |l_1 l_2 + m_1 m_2 + n_1 n_2|$.Substituting the given values,we get $\cos 	heta = |a_1 a_2 + b_1 b_2 + c_1 c_2|$.Since the denominator is $\sqrt{a_1^2 + b_1^2 + c_1^2} \cdot \sqrt{a_2^2 + b_2^2 + c_2^2} = \sqrt{1} \cdot \sqrt{1} = 1$,the expression simplifies to $|a_1 a_2 + b_1 b_2 + c_1 c_2|$.

If $(a_1, b_1, c_1)$ and $(a_2, b_2, c_2)$ are the direction cosines of two lines making an angle $\theta$ with each other,then $\cos \theta =$

Similar Questions

If a line makes angles $\alpha, \beta, \gamma$ with the coordinate axes,then $\cos 2\alpha + \cos 2\beta + \cos 2\gamma = \dots$

If the angles made by a straight line with the coordinate axes are $\alpha, \frac{\pi}{2}-\alpha, \beta$, then $\beta$ is equal to

If two straight lines whose direction cosines are given by the relations $l+m-n=0$ and $3l^{2}+m^{2}+cnl=0$ are parallel,then the positive value of $c$ is

Fill in the blanks:
The coordinates of points in the $XY$-plane are of the form ...........

The angle between the lines whose direction ratios are proportional to $(1, 2, 1)$ and $(2, -3, 6)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module